Remarks on the critical Besov space and its embedding into weighted Besov–Orlicz spaces

Hidemitsu Wadade
2010 Studia Mathematica  
We present several continuous embeddings of the critical Besov space B n/p,ρ p (R n ). We first establish a Gagliardo-Nirenberg type estimate into the weighted Besov space B 0,ρ p,wn (R n ) with the critical weight wn(x) = 1/|x| n ; more precisely, we prove B n/p,ρ p (R n ) → B 0,ρ p,Ws (R n ) with the weight Ws(x) = 1 |x| n [log(e+1/|x|)] s for any s > 1. 2010 Mathematics Subject Classification: Primary 46E35; Secondary 26D15.
doi:10.4064/sm201-3-2 fatcat:62dvsa5vybb4da5wdd7xprjdwu